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Social structures emerge as a result of individuals managing a variety ofdifferent of social relationships. Societies can be represented as highlystructured dynamic multiplex networks. Here we study the dynamical origins ofthe specific community structures of a large-scale social multiplex network ofa human society that interacts in a virtual world of a massive multiplayeronline game. There we find substantial differences in the community structuresof different social actions, represented by the various network layers in themultiplex. Community size distributions are either similar to a power-law orappear to be centered around a size of 50 individuals. To understand theseobservations we propose a voter model that is built around the principle oftriadic closure. It explicitly models the co-evolution of node- andlink-dynamics across different layers of the multiplex. Depending on link- andnode fluctuation rates, the model exhibits an anomalous shattered fragmentationtransition, where one layer fragments from one large component into many smallcomponents. The observed community size distributions are in good agreementwith the predicted fragmentation in the model. We show that the empiricalpairwise similarities of network layers, in terms of link overlap and degreecorrelations, practically coincide with the model. This suggests that severaldetailed features of the fragmentation in societies can be traced back to thetriadic closure processes.

Dynamical origins of the community structure of multi-layer societies